$\dfrac{1 - \cos^2\theta}{\cos^2\theta} = \; ?$
Answer: We can use the identity ${\sin^2 \theta} + {\cos^2 \theta} = 1$ to simplify this expression. $1$ ${\sin\theta}$ ${\cos\theta}$ $\theta$ We can see why this is true by using the Pythagorean Theorem. So, $1 - \cos^2\theta = \sin^2\theta$ Plugging into our expression, we get $ \dfrac{1 - \cos^2\theta}{\cos^2\theta} = \dfrac{\sin^2\theta}{\cos^2\theta} $ This is $\tan^2\theta$.